Most printers are exclusively binary in nature. In such apparatus, a binary one typically represents a black dot and a binary zero is a white dot, namely a blank. However, images obtained with scanning devices, such as a scanner, are generally non-binary gray scale images, namely containing pixel data of non-binary type, but multi-valued. Taking mono-scanning device as an example, if a pixel of a scan-in image is to be represented by 8 bits, then the pixel may have a value selected from one of 2.sup.8 =256 gray levels. In other words, the image is digitized into 256 gray levels by the scanning device, the lowest level, 0, being generally the darkest level, while the highest level, 255, is the lightest. In that case, the gray scale image so obtained cannot be printed directly with the binary printers for the non-binary data type of the image is inconsistent with the binary characteristic of the printer. An algorithm must be adopted to convert the gray scale image into a counterpart binary one and thus having a printing of variable shading. Such an algorithm is generally known as halftoning.
The halftoning technique has been widely discussed in the textbook "DIGITAL HALFTONING" of Robert Ulichney, published by MIT Press. in 1987. One of the halftoning techniques is proposed by Robert Floyd and Louis Steinberg in their paper "An Adaptive Algorithm for Spatial Gray Scale", SID INTERNATIONAL SYMPOSIUM DIGEST OF TECHNICAL PAPERS, pp. 36-37, 1975, which is generally called the error diffusion method and an illustrative processing algorithm of which is: ##EQU1## where A[i,j] is the element of an m.times.n original gray scale image array in which intensity values are between 0 and 1, B[i,j] is the element of an m.times.n binarized image array in which intensity values are either 0 or 1 (0 indicating a black dot and 1 a blank), thresh is the binarization threshold, and alpha, beta, gamma, and delta are weighting factors. The suggested values of these weighting factors by Floyd and Steinberg are: alpha 7/16, beta 3/16, gamma 5/16, and delta 1/16. It should be noted that the sum of these factors should be equal to one to give a zero overall error.
The disadvantages of the conventional error diffusion method include (1) the printed image is too dark to distinguish the details thereof, especially for the portion with lower gray level values and (2) the white background of the printed image is disturbed by snake-like noises.
Some patents try to overcome these disadvantages of error diffusion, such as U.S. Pat. Nos. 4,449,150 and 4,975,786. In U.S. Pat. No. 4,449,150, a random number is generated to be the threshold of the error diffusion. This avoids excessive dispersion of high frequency components in output pictures. In U.S. Pat. No. 4,975,786, a threshold value is set. When the pixel concentration is smaller than the threshold value, the error data generated for that pixel is set to 0, with the result that particles-like noises in the high contrast portion are eliminated and the encoding efficiency in highlight portions is improved.
To overcome the drawback of darkening, Robert Ulichney proposes in his book "DIGITAL HALFTONING" (pp. 11-13) a method to adjust the tone scale of the printed image which however enhances the contrast of the image only and not effectively improve the darkening problem.